# Time averaged distribution of a discrete-time quantum walk on the path

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- Limit theorems for decoherent two dimensional quantum walks. Ampadu, Clement // Quantum Information Processing;Dec2012, Vol. 11 Issue 6, p1921
In this paper we consider the model with decoherence operators introduced by Brun et al. (Phys Rev A 67:032304, ) which has recently been considered in the two-dimensional setting by Ampadu (Commun Theor Phys, ) to obtain the limit of the decoherent quantum walk.

- Quantum Algorithm for Modified Three-dimensional Random Walk Problem by Central Limit Theorem. Fujimura, Toru // Global Journal of Pure & Applied Mathematics;2012, Vol. 8 Issue 5, p501
A quantum algorithm for a modified three-dimensional random walk problem by the central limit theorem and its example are reported. When a random variable Vi [1 â‰¤ i â‰¤ n. i and n are integers.] becomes (1, 1, 1), (-1,-1,-1), (-1, 1, 1), (1,-1,-1), (-1,-1, 1), (1, 1,-1), (1,-1, 1) and...

- Limit Theorems for Open Quantum Random Walks. Konno, Norio; Yoo, Hyun // Journal of Statistical Physics;Jan2013, Vol. 150 Issue 2, p299
We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of SchrÃ¶dinger-Heisenberg representation in quantum mechanics. By this, we can compute...

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We treat three types of measures of the quantum walk (QW) with the spatial perturbation at the origin, which was introduced by Konno (Quantum Inf Proc 9:405, ): time averaged limit measure, weak limit measure, and stationary measure. From the first two measures, we see a coexistence of the...

- One-sided local large deviation and renewal theorems in the case of infinite mean. Doney, R. A. // Probability Theory & Related Fields;1997, Vol. 107 Issue 4, p451
Summary. If {S[sub n] ,nâ‰§0} is an integer-valued random walk such that S[sub n] /a[sub n] converges in distribution to a stable law of index Î±âˆˆ (0,1) as nâ†’ âˆž, then Gnedenkoâ€™s local limit theorem provides a useful estimate for P{S[sub n] =r} for values of r such...

- Quantum communication without the necessity of quantum memories. Munro, W. J.; Stephens, A. M.; Devitt, S. J.; Harrison, K. A.; Nemoto, Kae // Nature Photonics;Nov2012, Vol. 6 Issue 11, p777
Quantum physics is known to allow for completely new ways to create, manipulate and store information. Quantum communication-the ability to transmit quantum information-is a primitive necessary for any quantum internet. At its core, quantum communication generally requires the formation of...

- Quantum Algorithm for Modified One-dimensional Random Walk Problem by Central Limit Theorem. Fujimura, Toru // Global Journal of Pure & Applied Mathematics;2012, Vol. 8 Issue 4, p365
A quantum algorithm for a modified one-dimensional random walk problem by the central limit theorem and its example are reported. When a random variable Xi [1â‰¤ i â‰¤n. i and n are integers.] becomes dt and -dt [dt is a distance. 1 â‰¤ t â‰¤ k. t and k are integers.] as each...

- Quantum Algorithm for Modified Two-dimensional Random Walk Problem by Central Limit Theorem. Fujimura, Toru // Global Journal of Pure & Applied Mathematics;2012, Vol. 8 Issue 4, p401
A quantum algorithm for a modified two-dimensional random walk problem by the central limit theorem and its example are reported. When a random variable Vi [1â‰¤ i â‰¤ n. i and n are integers.] becomes dx,d-x,dy and d-y [distances of x, -x, y and -y directions, respectively] on an x - y...

- Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle. Chandrashekar, C.; Busch, Th. // Quantum Information Processing;Oct2012, Vol. 11 Issue 5, p1287
We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle system resembles the single-particle quantum walk...